The present invention relates in general to a system and to a method for encoding and decoding a signal and also to a method for transmitting signals from one location to another. In particular, it relates to a system and to a method for encoding and decoding a signal which increases the acceptable bandwidth of many systems without increasing the sampling rate thereof and without the effect of aliasing.
There are a large number of applications in which a fundamentally analog and generally repetitive signal must be quantized or sampled in temporal terms, for example, for subsequent recording, transmission and/or processing. This sampling in the time domain is often, but not necessarily, associated with digitization of the signal according to some algorithm. The need for sampling analog signals may arise, for example, in the areas of mensuration, communications, signal analysis, and synthesis.
The prior art has generally employed techniques in which sampling was accomplished at a constant rate: The prior art has also determined the maximum time between samples to accurately capture the information content of signals in a given bandwidth by resort to a theorem developed by Nyquist. The Nyquist theorem states, in effect, that the full informational content of a signal within a given bandwidth .DELTA.F can be captured only if ##EQU1## where T is the intersample period. Therefore, for any given bandwidth, the time between samples must be less than a given maximum value and accordingly the sampling rate must be greater than a given minimum value for the full informational content of the sampled signal to be captured. Once the sampling rate of any system has been determined according to the Nyquist theorem for a particular bandwidth, if a signal having a frequency outside the bandwidth is presented to the system, the phenomenon of aliasing occurs. Aliasing is a phenomenon in which the signal is reflected in the frequency domain about the upper corner frequency (1/2T) or its harmonics.
It would be desirable to provide a signal encoding and decoding system and method which minimizes the effect of aliasing when signals having a frequency outside a selected bandwidth are presented to the system. One possible means of achieving this objective would be merely to increase the sampling rate of the system, thereby increasing the bandwidth thereof. However, the maximum sampling rate of a system is typically determined by hardware limitations on digitizer settling rates (cross-talk) or alternatively digital communication or data transfer bit-rate limitations. Accordingly, one cannot increase the sampling rate in any given system without limit so as to increase the bandwidth.
It would be desirable to provide a signal encoding and decoding technique which would permit the sampling of signals having frequencies greater than the bandwidth of systems operating at their maximum sampling rate.